Quiz Question

One of a continuing series

We were given this problem in physics. Here is an explanation:

This is a standard principle of physics. See the image. A (hypothetical) light wave front from a source far away is incident on a solid wall. The wave crests are for the purposes of this demonstration parallel. The waves that hit the wall are stopped or reflected, and the remaining ones keep going as before:

Diffraction-01

Not really. The next figure shows what’s wrong with that interpretation. Considering the light wave as an electrical and magnetic field traveling through space, then the arrow points to a place adjacent to the electrical field that is vacant. The electric field will propagate into this space.

Diffraction-02

See the next figure. The wave front adjacent to the edge of the wall will curve toward the available space, effectively bending the wave front.

Diffraction-03

Here’s the result of this action. If you take a metal plate and make a small hole in it and then aim a beam of light at the hole, some light will pass through the hole. If the light is monochromatic, and you place a screen to the right of the plate in the figure, then you will see that the illumination on the screen conforms to the graph in the next figure. I copied this figure from Wikipedia and did some slight editing:

Diffraction1

Well and good. Now suppose you use electrons (or protons) instead of light waves. The same thing happens. See the next figure:

Diffraction-04

These electrons (electrons are round and black) and are headed for the hole in single file, but when they emerge from the hole they spread out like shot from the muzzle of a shotgun. Why?

The standard answer is that on a certain level electrons, in fact all particles and even macro objects, behave like waves. We were given the problem of deriving the diffraction of electrons (any sub-atomic particle for that matter).

While I was taking the course I went around and bought up a bunch of other physics books. One of them had a novel way of approaching this problem. It did not involve treating the electrons as waves. How else can you derive the diffraction pattern without resorting to wave analysis? I will give a hint later this week.

UPDATE

Enough of this. The answer lies in application of the Heisenberg uncertainty principle. Also in paying attention. This Quiz Question was resolved in a previous post, which discusses the diffraction of particles due to Heisenberg’s uncertainty principle.

4 thoughts on “Quiz Question

  1. One of those books you might have bought may be written by Richard Feynman. The electrons move backward and forward in time — as positrons — and every which way they want, which he called world lines. They might even revolve around Jupiter a few times before they come back, however small that chance might be. Hence, the diffusion is a consequence of what they do. I think they moving through two holes at once might explain it better.

  2. Fresnel diffraction at a straight edge:

    http://astarmathsandphysics.com/a-level-physics-notes/177-optics/2920-fresnel-diffraction.html

    When a star is occulted by the moon, if the star is not a point source, then the observed diffraction pattern can give an estimate of the angular diameter of the star.

    Google “Nather angular diameter of a star”
    Or “Nather Photoelectric Measurements of Lunar Occultations”

    http://link.springer.com/chapter/10.1007%2F978-94-010-3102-8_72#page-1

    • Mike,

      Thanks for posting this. I knew Ed Nather. When I worked at the UT Astronomy Department he came to work there. He was an electrical engineer with a great interest in astronomy. He had a nice Questar system and was passionate about viewing. He was on a team of about four who published the first paper confirming water in the Mars atmosphere.

      Lunar occultations were at the time and still are a valuable means for getting a refined view of distant stars. Optical telescopes are diffraction-limited due to their limited aperture. Using the mountains of the moon as occulting objects allowed observers to overcome this limitation. When a critical occultation was due great preparations were made for the event. There is no rescheduling such an event, and preparation was critical. The researchers could only hope there would be no clouds.

      So, that was a nice discourse on optical diffraction. What about the diffraction of sub-atomic particles passing through small apertures?

  3. Pingback: Quiz Question | Skeptical Analysis

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